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Complex Analysis and Operator Theory最新文献

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Strong b-Suprametric Spaces and Fixed Point Principles 强 b 超空间和定点原理
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-09-04 DOI: 10.1007/s11785-024-01594-2
Maher Berzig
{"title":"Strong b-Suprametric Spaces and Fixed Point Principles","authors":"Maher Berzig","doi":"10.1007/s11785-024-01594-2","DOIUrl":"https://doi.org/10.1007/s11785-024-01594-2","url":null,"abstract":"<p>In this paper, we introduce the strong <i>b</i>-suprametric spaces in which we prove the fixed point principles of Banach and Edelstein. Moreover, we prove a variational principle of Ekeland and deduce a Caristi fixed point theorem. Furthermore, we introduce the strong <i>b</i>-supranormed linear spaces in which we establish the fixed point principles of Brouwer and Schauder. As applications, we study the existence of solutions to an integral equation and to a third-order boundary value problem.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Conditions Implying Self-adjointness and Normality of Operators 意味着算子自相接和规范性的条件
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-09-04 DOI: 10.1007/s11785-024-01596-0
Hranislav Stanković
{"title":"Conditions Implying Self-adjointness and Normality of Operators","authors":"Hranislav Stanković","doi":"10.1007/s11785-024-01596-0","DOIUrl":"https://doi.org/10.1007/s11785-024-01596-0","url":null,"abstract":"<p>In this paper, we give new characterizations of self-adjoint and normal operators on a Hilbert space <span>(mathcal {H})</span>. Among other results, we show that if <span>(mathcal {H})</span> is a finite-dimensional Hilbert space and <span>(Tin mathfrak {B}(mathcal {H}))</span>, then <i>T</i> is self-adjoint if and only if there exists <span>(p&gt;0)</span> such that <span>(|T|^ple |textrm{Re},(T)|^p)</span>. If in addition, <i>T</i> and <span>(textrm{Re},T)</span> are invertible, then <i>T</i> is self-adjoint if and only if <span>(log ,|T|le log ,|textrm{Re},(T)|)</span>. Considering the polar decomposition <span>(T=U|T|)</span> of <span>(Tin mathfrak {B}(mathcal {H}))</span>, we show that <i>T</i> is self-adjoint if and only if <i>T</i> is <i>p</i>-hyponormal (log-hyponormal) and <i>U</i> is self-adjoint. Also, if <span>(T=U|T|in mathfrak {B}({mathcal {H}}))</span> is a log-hyponormal operator and the spectrum of <i>U</i> is contained within the set of vertices of a regular polygon, then <i>T</i> is necessarily normal.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"37 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rough Singular Integral Operators, Spherical Maximal Functions and Maximal Bochner-Riesz Operators on Grand Morrey Spaces 大莫里空间上的粗糙奇异积分算子、球面最大函数和最大波赫纳-里兹算子
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-09-02 DOI: 10.1007/s11785-024-01588-0
Kwok-Pun Ho
{"title":"Rough Singular Integral Operators, Spherical Maximal Functions and Maximal Bochner-Riesz Operators on Grand Morrey Spaces","authors":"Kwok-Pun Ho","doi":"10.1007/s11785-024-01588-0","DOIUrl":"https://doi.org/10.1007/s11785-024-01588-0","url":null,"abstract":"<p>This paper extends the Rubio de Francia extrapolation method to the grand Morrey spaces on Euclidean spaces. By using this extended extrapolation method, we obtain the boundedness of the rough singular integral operators, the spherical maximal functions and the maximal Bochner-Riesz operators on the grand Morrey spaces on Euclidean spaces.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"12 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Linear Recurrence of (Generalized) Hybrid Numbers Sequences and Moment Problems 论（广义）混合数列的线性递推和矩问题
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-08-31 DOI: 10.1007/s11785-024-01582-6
Abdallah Taia, Rajae Ben Taher, Bouazza El Wahbi
{"title":"On the Linear Recurrence of (Generalized) Hybrid Numbers Sequences and Moment Problems","authors":"Abdallah Taia, Rajae Ben Taher, Bouazza El Wahbi","doi":"10.1007/s11785-024-01582-6","DOIUrl":"https://doi.org/10.1007/s11785-024-01582-6","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Aim</h3><p>The aim of this study is to introduce definitions and explore properties of moment problems for sequences of generalized hybrid numbers satisfying a linear recursive equation.</p><h3 data-test=\"abstract-sub-heading\">Methods</h3><p>We analyze complex measures derived from the linear recurrence of hybrid numbers and generalized hybrid numbers sequences.</p><h3 data-test=\"abstract-sub-heading\">Results</h3><p>We present results pertaining to the moments of these complex measures.</p><h3 data-test=\"abstract-sub-heading\">Conclusions</h3><p>This study contributes to the understanding of moment problems in the context of generalized hybrid number sequences.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"2 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Structure of Real Operators 论实数算子的结构
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-08-30 DOI: 10.1007/s11785-024-01592-4
Ying Yao, Luoyi Shi
{"title":"On the Structure of Real Operators","authors":"Ying Yao, Luoyi Shi","doi":"10.1007/s11785-024-01592-4","DOIUrl":"https://doi.org/10.1007/s11785-024-01592-4","url":null,"abstract":"<p>An operator <i>T</i> on a complex separable Hilbert space <span>({mathcal {H}})</span> is called a real operator if <i>T</i> can be represented as a real matrix relative to some orthonormal basis of <span>({mathcal {H}})</span>. In this paper, we provide descriptions of concrete real operators, such as real normal operators, real partial isometries, and real Toeplitz operators, among others. Furthermore, we present several structure theorems of real operators, including the polar decomposition, the Riesz decomposition and the block structure.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"59 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some Operators on Minimal $$alpha $$ -Möbius Invariant Function Spaces 最小 $$α $$ - 莫比乌斯不变函数空间上的一些算子
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-08-29 DOI: 10.1007/s11785-024-01587-1
Zengjian Lou, Xiaojing Zhou
{"title":"Some Operators on Minimal $$alpha $$ -Möbius Invariant Function Spaces","authors":"Zengjian Lou, Xiaojing Zhou","doi":"10.1007/s11785-024-01587-1","DOIUrl":"https://doi.org/10.1007/s11785-024-01587-1","url":null,"abstract":"<p>In this paper, our primary focus is to study the boundedness and compactness of Volterra type operators and multiplication operators on minimal <span>(alpha )</span>-Möbius invariant function spaces. Additionally, we also present a characterization of the boundedness and compactness of Volterra type and multiplication operators from minimal <span>(alpha )</span>-Möbius invariant function spaces to Besov spaces.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"97 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Periodic Functions: Self-Intersection and Local Singular Points 周期函数：自交和局部奇异点
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-08-26 DOI: 10.1007/s11785-024-01586-2
Lev Sakhnovich
{"title":"Periodic Functions: Self-Intersection and Local Singular Points","authors":"Lev Sakhnovich","doi":"10.1007/s11785-024-01586-2","DOIUrl":"https://doi.org/10.1007/s11785-024-01586-2","url":null,"abstract":"<p>Self-intersections and local singular points of the curves play an important role in algebraic geometry and many other areas. In the present paper, we study the self-intersection and local singular points of the <i>n</i>-member chains. For this purpose, we derive and use several new results on trigonometric formulas. A unified approach for calculating self-intersection and local singular points for a wide class of curves is presented. An application to the spectral theory of integro-differential operators with difference kernels is given as well.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Research Story 研究故事
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-08-24 DOI: 10.1007/s11785-024-01580-8
Alexander Kheifets
{"title":"A Research Story","authors":"Alexander Kheifets","doi":"10.1007/s11785-024-01580-8","DOIUrl":"https://doi.org/10.1007/s11785-024-01580-8","url":null,"abstract":"<p>A story of the joint research that led to the setting and solution of the Abstract Interpolation Problem.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"32 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Generalized Toeplitz Determinants for a Class of Holomorphic Mappings in Several Complex Variables 几种复变量中一类全态映射的广义托普利兹决定因素
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-08-19 DOI: 10.1007/s11785-024-01585-3
Qinghua Xu, Ting Jiang
{"title":"The Generalized Toeplitz Determinants for a Class of Holomorphic Mappings in Several Complex Variables","authors":"Qinghua Xu, Ting Jiang","doi":"10.1007/s11785-024-01585-3","DOIUrl":"https://doi.org/10.1007/s11785-024-01585-3","url":null,"abstract":"<p>In this paper, we define the generalized Toeplitz determinants whose entries are the coefficients of holomorphic functions on the unit disk <span>(mathbb {U})</span> with <i>k</i>-fold symmetric, and then we establish the sharp bounds of the generalized determinants formed over the related terms of homogeneous expansion of a class of holomorphic mappings defined on the unit ball of a complex Banach space. The results presented here would generalize the corresponding results given by Giri and Kumar (Complex Anal Oper Theory 17(6):86, 2023).</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"38 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Extended Joint Numerical Radius of the Spherical Aluthge Transform 扩展的球面阿鲁什变换联合数值半径
IF 0.8 4区 数学
Complex Analysis and Operator Theory Pub Date : 2024-08-14 DOI: 10.1007/s11785-024-01583-5
Bouchra Aharmim, Yassine Labbane
{"title":"Extended Joint Numerical Radius of the Spherical Aluthge Transform","authors":"Bouchra Aharmim, Yassine Labbane","doi":"10.1007/s11785-024-01583-5","DOIUrl":"https://doi.org/10.1007/s11785-024-01583-5","url":null,"abstract":"<p>Let <span>(T=(T_{1}, T_{2},ldots , T_{n}))</span> be a commuting <span>(n-)</span>tuple of operators on a complex Hilbert space <i>H</i>. We define the extended joint numerical radius of <i>T</i> by </p><span>$$begin{aligned} J_{t}w_{(N, v)}(T)=sup limits _{(lambda _{1}, lambda _{2}, ldots , lambda _{n})in overline{B_{n}}(0, 1)}w_{(N, v)}bigg (sum limits _{i=1}^{n}lambda _{i}T_{i}bigg ), end{aligned}$$</span><p>where <i>N</i> is any norm on <i>B</i>(<i>H</i>), </p><span>$$w_{(N, v)}(S)=sup limits _{theta in mathbb {R}}N(ve^{itheta }S+(1-v)e^{-itheta }S^{*}), Sin B(H), vin [0, 1],$$</span><p>and <span>(overline{B_{n}}(0, 1))</span> denotes the closure of the unit ball in <span>(mathbb {C}^{n})</span> with respect to the euclidean norm, i.e. </p><span>$$overline{B_{n}}(0, 1)=left{ lambda =(lambda _{1}, ldots , lambda _{n})in mathbb {C}^{n}; parallel lambda parallel _{2}=bigg (sum limits _{i=1}^{n}|lambda _{i}|^{2}bigg )^{frac{1}{2}}le 1 right} .$$</span><p>In this paper, we prove several inequalities for the extended joint numerical radius involving the spherical Aluthge transform in the case where <i>N</i> is the operator norm of <i>B</i>(<i>H</i>) or the numerical radius.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"18 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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